Grind star anise and coriander seeds in spice mill or with mortar and pestle. Slice chile and garlic, then mash to a paste using the side of a chef's knife. Transfer to a small bowl and stir in ground spices, soy sauce, fish sauce, and paprika.
Lightly score pork skin crosswise in a tight pattern with a very sharp knife, cutting through the skin and some fat, but taking care not to slash the meat itself. Transfer pork to a large Dutch oven with a tight-fitting lid or a roasting pan. Season liberally with salt and pepper and rub with marinade. Cover (use foil with roasting pan) and chill overnight.
Preheat oven to 425°F. Place pork, covered, in oven; reduce oven temp to 300°F. Roast pork, basting with juices every hour, until meat is fork-tender and bones are very loose, 5–5 1/2 hours.
Uncover pork and increase temperature to 450°F. Roast, basting every 5 minutes and adding water by 1/4-cupfuls if juices become syrupy, until pork is dark brown and skin is crisp, 15–20 minutes.
Carefully transfer pork to a platter. Skim fat from pan juices and pour remaining juices over.
